Let the length of a rectangle be
l and the width of that rectangle be
w, then the area of the rectangle is given by:

In our problem,
l= 9 inches, and
w=4.25 inches.
then,

(square inches)
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Remark: we performed the following operation to make the multiplication easier:

we wrote 4.25 as 4+0.25, and multiplied 9 to each of these separately, instead of multiplying 9 to 4.25 directly, using the distributive property
thus making the operation a little easier.
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Answer: 38.25 square inches
Remark :
Asking "Round to the correct significant digits" is not correct.
The number of significant digits must be stated.
if we want the number rounded to 3 significant digits 38.25 is 38.6
if we want the number rounded to 2 significant digits 38.25 is 38.0
if we want the number rounded to 1 significant digits 38.25 is 40,0